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Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space.
Keywords: superintegrability; quadratic algebras. 
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     author = {Ernest G. Kalnins and Jonathan M. Kress and Willard Miller Jr. and Sarah Post},
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}
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Ernest G. Kalnins; Jonathan M. Kress; Willard Miller Jr.; Sarah Post. Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a7/

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